I'd join you but I don't have my Clubs with me
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As far as options, Harborside is probably your best bet but it is still about a 30 min drive from the Loop and on the other side of the city from OHare. It'd be more economical to just rent a Zipcar or something instead of a cab / uber for that distance.
I can't really weigh-in on what is open and what isn't open but I'd recommend maybe checking out the thread at GolfWRX about Chicago golf. It's quite active and I've met a few good guys from that forum and they have great advice.